Three dimensional analysis of the vibration characteristics of piezoelectric discs

Abstract

The piezoelectric transducer plays a paramount role in the ultrasonic non-destructive testing systems which are increasingly employed in industry. The active element in these transducers is the piezoelectric disc and its vibration characteristics govern the performance of the transducer. One dimensional theory (lD) [1], which assumes that the piezoelectric disc vibrates in the thickness direction only as shown in Fig 1, has been used for many years. However, the lD theory cannot predict other vibration modes, which may affect the transducer behaviour in the frequency range of interest, especially for those transducers with a small diameter to thickness (Orr) ratio.There have been many experimental reports which show that a variety of vibration modes exist in piezoelectric discs [2][3][4]. It has been found that there are five types of mode in the frequency range of interest; these are radial (R), edge (E), thickness shear (TS), thickness extensional (TE) and high frequency radial (A) modes. The vibration characteristics of piezoelectric discs have been analysed by three dimensional analytical theory [5], and two dimensional plate theory [6,7]. Although there is generally good agreement between the predictions by the plate theory and the measurements [3,6], some modes are not predicted accurately and the strength of excitation of the different modes has not been predicted. Finite element analysis, which was first developed for piezoelectric materials by Allik [8], has also been applied to piezoelectric discs [9,10]. However, the piezoelectric discs studied were of relatively small orr ratio, and the frequency response functions, which enable the strength of excitation of the different modes to be determined, were not predicted.In this paper the vibration characteristics of piezoelectric discs are analysed by a three dimensional fmite element model, and the electrical impedance functions of PZT5A discs with orr ratios of 20 and 10 are calculated. The calculations are checked by experimental measurements. ANALYSISThe general finite element formulation for piezoelectric materials has been given by Allik [8]. Since then it has been used in analyses of many piezoelectric devices. However, those fmite element models usually used a mass condensation scheme to eliminate the static electrical